The reason is: Vehicle must be syncronized with group. Can be done in Editor.
I see the issue if you are like me. Don't have time to use editor. I prioritize play the game and all the great missions and scenarios you guys/girls out there are making. Thank you.
If you in game(f. ex a whole lot of altis or dynamic universial war system) have a function that can assign/unassign to HC. If you mount the group into a vehicle, and assign the group to HC, they now are able to use transport. As Get in/out command. Problem is: The group has to drive the vehicle them self. You as a commander can't have a transport unit.
I guess when you assign the group to HC inside the vehicle they get sync.